Thursday, March 17, 2011

Mathematically Proven Fact: Accelerate While Turning

Today I was chit chatting with my mentor about curvature and other differential-geometry-related shtuff, when she told me a most surprising fact. Unfortunately I can not explain it without relying on abstract mathematical concepts, because I myself can only understand it in those terms. It's really counterintuitive. Imagine you're driving on an exit ramp (or any any curved road for that matter). You want your acceleration vectors to point towards where you want your car to go, which in this case would be centripetally, towards the center of the circle in which you're driving. If you speed up, the acceleration vector gets longer, and pushes you more strongly to the center. If you decelerate, however, your acceleration vectors point backwards, away from where you want to go, so your car starts to skid. Of course it's good to slow down before making a turn. But once you start turning, you want to speed up. I'm talking nonsense? Well, that's what SHE said.

To understand this, do the following experiment:
Take a deep breath.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
Oh no! You're going to fast! You gently push the break.
Visualize it.
What do you feel happening?
I feel the tail of car swerving off the road.

Now let's try this again.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
As you start curving, you press the accelerator.
Visualize it.
What do you feel happening?
I feel the car griping the road.

These thought experiments are really worthless. It's possible that the reason I connect decelerating with losing control is because I usually slow down only if I'm going too fast to begin with. And I connect accelerating with control because I usually accelerate only if I started off at a slow enough speed. It's a shame she didn't tell me about this when I met with her last Wednesday. That way I could have experimented when I drove to Pittsburgh last Thrusday. All my passengers were screaming that I drive too fast. Wouldn't they love it if I told them that taking curves fast is safer? And then proceeded to demonstrate it experimentally?

But the bottom line is: you should definitely slow down before the curve. And if you are pulled over for speeding through a curve, explain to the cop that if you would have slowed down, you would have skidded off the road. Then pull out a pad and draw the acceleration vectors. The cop should excuse you, because math never lies.

66 comments:

  1. But even with all the calculations, will you ever be ahead of the curve?

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  2. So if you ever feel like road-trippin to Oregon, there's a fantastic desert you can zip through. I recall going 105 with just a permit.

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  3. Yehuda: you must be using some RSS subscription if you commented so fast. Who are you?

    Sara: One of the schools I applied to for the summer was in Oregon, and I thought of spending time in your lovely state. But UCSB won. sorry.

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  4. Your loss! You could have met Pierre.

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  5. Indeed, I use google reader.

    You don't know me, I don't know you (as far as I know). I found you through TRS where, much like here, I lurk and comment infrequently.

    I enjoy reading your stuff, hope you don't mind my interjections.

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  6. Um, doesn't everyone know this, that you accelerate coming through and out of a curve? Heck, I don't even have a driving license, and I know this.

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  7. watch out for newton's 3rd law.

    btw i also use google reader and im sure that there are many others, so you probably have a lot more readers than you think.

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  8. I'm with TRS. I always speed up in my curve and out. I never knew it was because I'm a math genius.

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  9. TRS: No, not everyone knows it.

    Sarabonne: Pierre? As in the guy who lives near the Hudson River and collects cats?

    To the lurkers: According to Google I have 39 subscribers. Yeah, I guess I always knew people like you exist, but it's a bit of a shock to actually see you.

    CB: what about Newton's third law?

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  10. That's another Pierre, this Pierre has two wheels and a seat.

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  11. oh! your dad's motorcycle?

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  12. Now way, that's Regina.
    Pierre is my barely used bike waiting patiently for me back home.

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  13. Oops! that should have been Newton 2nd law.
    The force that keeps the car moving on the circle is F= ma (where a is the vector directed towards the center) and is supplied by the static friction between the tires and the road. now if you accelerate too much you will exceed the maximum static friction and your car will start to slide and you will begin traveling on a path tangent to the circle (or close to that since you would still have the lesser kinetic friction).

    for example, the static friction between you and the seat has a considerably smaller static friction coefficient, so when you do a sharp turn you continue on a path tangent to the turn and the seat simply slides out from beneath you.

    I hope I'm not too confusing...

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  14. Sarabonne: So dad's motorcycle is female and your bike male? Non-traditional gender roles in your family...

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  15. Oh! It's my old friend Chassidic Bochur! I no longer feel stalked by hidden reader readers.

    Anyhow, IIRC what I learned in Physics I, that business with the acceleration being to big for the static friction doesn't take into account the direction of the acceleration. But what I'm saying in this post is all about the direction. If you accelerate with some fixed magnitude, but with the vector pointing behind you (a.k.a. decelerating) that will have a greater skidding affect than if you accelerate with the same magnitude with the vector in front of you.

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  16. I'm making you feel stalked? Why, that is thrilling. I feel......intimidating. Almost powerful.

    This is a wonderful change from my usual timid self. Ah, the spring in the step I've always read and heard about...

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  17. Yehuda, there are more healthy ways to get your power rush.

    ReplyDelete
  18. like drugs! Health part excluded.

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  19. my comment was only intented to serve as a warning to anyone actually attempting to do the experiment to keep in mind that accelerating too much could be dangeruous.

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  20. Drug induced power rush. There are reasons why some people think they can fly.

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  21. AVAST ! Ye Mateys...

    ReplyDelete
  22. "Behold your doom cometh..."

    -Anagignoskomena

    ReplyDelete
  23. Behold, anon speaketh like a madman.

    ReplyDelete
  24. discount prescriptions rohypnol, Barbiturates and desoxyephedrine only at http://5z8.info/startphish_skt

    ReplyDelete
  25. Sheesh. I was scared for a second that the spambots had found me.

    ReplyDelete
  26. The harder you accelerate on the curve, the harder you'll have to break at the inflection points.

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  27. Hey Friend, its meMarch 28, 2011 at 11:50 PM

    http://5z8.info/ninjastaroutlet_b5j7yq_oneweirdoldtiptolosebellyfat

    Baby sectors IDVF2...Shaylaman

    ReplyDelete
  28. well there's one helpful piece of spam.

    ReplyDelete
  29. CA: Good point

    Anon: What's with the faux-spam?

    ReplyDelete
  30. Dear Sir, dear Madam-

    My name is Hadar, also called "The impossible" or sometimes "The destroyer". I rule over a small kongdom that exists-! -an Island, with abundant richness and wealth. I have two brothers , Ah-puk "the caretaker" and Bee-Wee-Celmentinus "whe who stuffs himself".

    To make a long story short, you have won our yearly lottery. congratulations! You can now claim your price.

    We will carve a statue of you(using only you.-it will look like a small train. I hope you understand(?). We have ways to do this!), caress you, take care of you as a king-for three days !- and then you shall die a slow death-"he who dances naked with the gods".

    I can assure you ,it excites me as much as it does you, and my hands tremble as I write. Oh, I can see you on that cliff- holding the "apple". ..

    We look forward to it with a stirn but happy expression on our faces, and hope you do the same

    take care

    Hadar "the impossible" Papoo

    ReplyDelete
  31. a=x
    a+a=a+x
    2a=a+x
    2a-2x=a+x-2x
    2(a-x)=a+x-2x
    2(a-x)=a-x
    2=1

    ReplyDelete
  32. http://books.google.com/books?id=obJ70nxVYFUC&lpg=PA219&ots=JMiE-QXa7k&dq=winston%20churchill%20is%20a%20carrot%20charles%20seife&pg=PA217#v=onepage&q&f=false

    ReplyDelete
  33. Let a,b,c,d be 4 consecutive integers.
    Find the square root of a×b×c×d + 1
    Let a,b,c,d = (n-1), n, (n+1), (n+2)

    (n-1) n (n+1) (n+2) + 1 =
    (n-1)(n+2) n (n+1) + 1 =
    (n^2+n - 2) (n^2+n) + 1 =
    (n^2+n)^2 - 2 (n^2+n) + 1 =
    (n^2+n - 1)^2
    The square root of which is n^2 + n - 1,
    or (n-1)(n+2) + 1.

    Example: let n = 18, and the numbers are 17,18,19,20.
    (n-1)(n+2)+1 = 17*20+1 = 341.

    17*18*19*20 + 1 =
    17*20 * 18*19 + 1 =
    340 * 342 + 1 =
    340 * (340+2) + 1 =
    340^2 + 2 * 340 + 1 =
    (340+1)^2 =
    341^2

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  34. anon, you're starting to piss me off. who are you?

    ReplyDelete
  35. wait, what did anon say that's so annoying?

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  36. He's being a pain, thinking he's so smart coming up with math tricks and fake spam.

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  37. Take any four consecutive numbers (e.g. 3, 4, 5, 6 or 100, 101, 102, 103), multiply them together, and then add one. The result will have an integer square root. To which I say, big deal!!

    Maybe I'm pissed because this Indian dude just wasted an hour of my time talking about so-called Vedic mathematics and Karma.

    ReplyDelete
  38. Eating cholov stams blocks up your chakras.

    ReplyDelete
  39. I know a good indian place if you're hungry...

    ReplyDelete
  40. Given the fifth term in the expansion of the binomial (a^4-3/a)^n contains the term a^4, determine n.

    ReplyDelete
  41. http://imgs.xkcd.com/comics/how_it_works.png

    ReplyDelete
  42. CA: ??

    Anon: now that's a good one. Let me think about it.

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  43. Anon: Now I really hate you. By the way, the answer is 6

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  44. Heehee, different anon. BTW you owe sarabonne a comment.

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  45. damn, that was also meant to be anonymous.

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  46. Timtum moach v'lev = blocking up chackras. You can tell that to your Indian friend. If he eats milk whose milking was not supervised by Jews, he will never reach Enlightenment.

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  47. CA: He's not Jewish, you know.

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  48. Are you saying his lev is metamtem to the maximum already?

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  49. That's not what I'm saying. Is that what you're saying?

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  50. I am not sure. Chassidus doesn't discuss much about goyim. It's not even clear that they have bechira. (According to science they for sure do not.)

    How late does the Chabad shull finish on Peisach for Shachris? I am wondering whether to go there or to my in-laws' shull.

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  51. Also, was the statistics cartoon about cancer?

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  52. CA: I hope you were joking when you said that according to science (davka) goyim don't have bechira. Either way, Toras Emes, Toras Chaim doesn't encourage them to drink cholov yisroel, so presumably it's not important for them.

    I think on shabbos they finish like 11:15-11:30. I suppose Yom Tov is similar.

    Many are the mysteries of this anon.

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  53. According to science, there is no such thing as bechira. All decisions that you make are deterministically determined by existing states of synaptic connections in your brain, genes expressed, your cellular architecture and the information that is entering the brain.

    Even if you say that some of these decisions are random in true sense of the word, that is still not bechira.

    ReplyDelete
  54. http://www.collive.com/pics/s_nf_9532_53251.jpg

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  55. Signing off, cap'nApril 5, 2011 at 6:05 PM

    I meant thus: 3.6260047920e-1

    sorry for the confusion.

    loves.

    this is the final broadcast

    ReplyDelete
  56. CA: And has science found that Jews' brains are different?

    Anon: Are you the one guy in the picture who I know? Or is that picture just another one of your mysteries?

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  57. CA: So you're planning on davening some things at your in-law's Shul and some at Chabad? Just remember to say Hallel the first two nights.

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  58. Why aren't math jokes good in base 8?

    because 7 10 11

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  59. TRS: the probability cloud of my davening on Peisach will be divided between Chabad and MO shulls of Skokie.

    e: I may actually need to find a place to go to for the seventh night study, as well as for the seudas Moshiach. Any thoughts?

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  60. re: brains: nope. I was not suggesting that acc. to science Jews have bechira. More like that bechira is a nonsensical concept, since either a system makes a decision deterministically or randomly. Either way doesn't help you.

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  61. there's learning at the Raices residence on the 7th night. There's a Moshiach Seudah at chabad on the 8th day. Dr. Ira Weiss's probability cloud is heavily concentrated at chabad on achron shel pesach, so do come.

    Aha, so according to science there is no such thing as bechirah. so why do you believe that there is?

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Forth shall ye all hold.